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A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2021 · Q610 Marks

The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below. Rebels 75 78 79 80 82 82 83 84 85 86 89 93 95 99 102 Sharks 66 68 71 72 74 75 75 76 78 83 83 84 85 86 92 A box-and-whisker plot for the Sharks is shown below. [Box-and-whisker plot for Sharks]

  1. (a)Represent the data by drawing a back-to-back stem-and-leaf diagram with Rebels on the left-hand side of the diagram.[4]
  2. (b)Find the median and the interquartile range for the Rebels.[3]
  3. (c)On the same diagram, draw a box-and-whisker plot for the Rebels.[2]
  4. (d)Make one comparison between the weights of the players in the Rebels club and the weights of the players in the Sharks club.[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [B1] Correct stem, ignore extra values (not in reverse).
  2. [B1] Correct Rebels labelled on left, leaves in order from right to left and lined up vertically, no commas.
  3. [B1] Correct Sharks labelled on same diagram, leaves in order and lined up vertically, no commas.
  4. [B1] Correct key for their diagram, need both teams identified and 'kg' stated at least once here or in leaf headings or title. SC If 2 separate diagrams drawn, SC B1 if both keys meet these criteria.
  5. [B1] Median = 84 (kg)
  6. [M1] [UQ = 93, LQ = 80] 93 – 80. 95 < UQ < 89 – 79 < LQ < 82
  7. [A1] [IQR =] 13 (kg) WWW
  8. [B1] Box and whisker with end points 75 and 102 Whiskers drawn to correct end points not through box, not joining at top or bottom of box.
  9. [B1 FT] Median and quartiles plotted as box graph.
  10. [B1] e.g. Average weight of Rebels is higher than average weight of Sharks. Acceptable answers refer to: Range, skew, central tendency within context. E.g. range of Rebels is greater B0. Range of weights of the rebels is greater B1. Simple value comparison insufficient.

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 5 Variant 1, question 6.

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